The code used is included as a separate file ‘supplementary_code.zip’, which contains two files suitable for building with a C++ compiler:• main.cpp, which is the main model code• mersenne_twister.h, which contains the Mersenne twister functionThe latter is an amended version of a library distributed under a GNU Library General Public License - please see the file header for details. from Leaving safety to visit a feeding site: is it optimal to hesitate while exposed?

Animals living in complex environments experience differing risks of predation depending upon their location within the landscape. An animal could reduce the risk it experiences by remaining in a refuge site, but it may need to emerge from its refuge and enter more dangerous sites for feeding and other activities. Here, I consider the actions of an animal choosing to travel a short distance between a safe refuge and a dangerous foraging site, such as a bird leaving cover to visit a feeder. Although much work has been conducted examining the choice between a refuge and a foraging site when faced with a trade-off between starvation and predation risk, the work presented here is the first to consider the travel behaviour between these locations. Using state-dependent stochastic dynamic programming, I illustrate that there are several forms of optimal behaviour that can emerge. In some situations, the animal should choose to travel without stopping between sites, but in other cases, it is optimal for the animal to travel hesitantly towards the food, and to stop its travel at a point before it reaches the refuge. I discuss how this hesitant ‘dawdling’ behaviour may be optimal, and suggest further work to test these predictions.